Computer graphics; computational geometry (digital and algorithmic aspects) \{For methods of numerical mathematics, see 65D18\}
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Can every convex polyhedron be flattened without overlap after cutting along one simple path through all its vertices? This zipper path may traverse face interiors, and is not required to follow the edge graph.
For each k , classify or construct all k -equiprojective polyhedra: polyhedra whose orthogonal projection is a k -gon in every direction not parallel to a face. The source already gives an edge-face-pair…
For a general-position set of n planar points, color every segment joining two points so that properly crossing segments have different colors. Determine the worst-case minimum number of colors as a function of n ;…
Must every closed polyhedral surface homeomorphic to S^2 , composed of congruent regular pentagons and immersed in mathbb R ^3 , arise as the boundary of a union of solid regular dodecahedra joined along whole faces?
A rectangular grid board assigns a value from one to six to every cell. Determine the complexity of deciding whether a standard labeled die, from the specified corner and initial orientation, can roll across the board…
For a planar point set S in general position, let rho(S) be the minimum number of reflex vertices in a simple polygon using exactly S as its vertices. Determine rho(n)= max |S|=n rho(S) . Is rho(n)= lfloor n/4 rfloor ?
Can every genus-zero polyhedron formed by joining unit cubes face to face be unfolded into one planar piece without overlap by cutting along exposed cube edges? All cube edges on the boundary are available, including…
Can a data structure maintain n planar points under insertion and deletion, and return the Euclidean nearest neighbor of any query point, with O( log n) time for each operation? Specify whether update guarantees are…
Among convex planar shapes of unit area, which yields the largest volume by perimeter-halving folding? Choose two boundary points that divide the perimeter equally and identify the two intervening boundary arcs by equal…
For a convex piece, define circularity as its smallest enclosing-circle radius divided by its largest inscribed-circle radius. Determine the infimum, over finite convex polygonal partitions of a square, of the largest…
These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.
Springer Nature
Discrete geometry and geometric computation
SIAM
Theory of computation
SIAM
Applied and computational mathematics reviews
2007 · 2 questions extracted
2020 · 0 questions extracted
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